ON RINGS DETERMINED BY ZERO PRODUCTS
ON RINGS DETERMINED BY ZERO PRODUCTS
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DOI：
10.1142/s0219498813500588
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发表时间：
2013-07
影响因子：
0.8
通讯作者：
H. Ghahramani
中科院分区：
文献类型：
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作者：
H. Ghahramani
做个戒指吧。我们称它是零积确定的，如果对每个可加群和每个双可加映射满足：如果当ab = 0时B）= 0，则存在一个可加映射使得对所有的都有B）= T（ab）。本文首先研究了零积确定环的性质，证明了半交换环和非交换环都不是零积确定的。然后，我们将研究是否有一个非平凡的幂等元的环是零积确定的。作为上述结果的应用，我们证明了具有非平凡幂等元的单环、满矩阵环和某些算子代数类是零积确定环，并讨论了三角环和上三角矩阵环是否是零积确定环.
Let be a ring. We say that is zero product determined if for every additive group and every bi-additive map the following holds: if ϕ(a, b) = 0 whenever ab = 0, then there exists an additive map such that ϕ(a, b) = T(ab) for all . In this paper, first we study the properties of zero product determined rings and show that semi-commutative and non-commutative rings are not zero product determined. Then, we will examine whether the rings with a nontrivial idempotent are zero product determined. As applications of the above results, we prove that simple rings with a nontrivial idempotent, full matrix rings and some classes of operator algebras are zero product determined rings and discuss whether triangular rings and upper triangular matrix rings are zero product determined.